Digital Signal Processing Reference
In-Depth Information
2.1.3.1 SISO/SIMO/MISO/MIMO Systems
This classification is based on the number of input and output signals of a
system:
•
SISO (single-input single-output) systems have a single input signal
and a single output signal. Therefore,
x
and
y
become scalars.
•
SIMO (single-input multiple-outputs) systems have a single input
signal and more than one output signal.
•
MISO (multiple-input single-output) systems have multiple input
signals and a single output signal.
•
Finally, MIMO (multiple-input multiple-output) systems have mul-
tiple input and output signals, and form the most general of the four
classes.
Throughout the topic, the reader will have the opportunity of considering
the differences between these classes of systems, the importance of which is
patent in modern signal processing techniques.
2.1.3.2 Causal Systems
If the system output depends exclusively on present and past values of the
input, the system is said to be
causal
. In other words, causality means that
the output of a system at a given instant is not influenced by future values of
the input.
When we consider real-time applications, causality will certainly hold.
However, when we manipulate acquired data, noncausal systems are accept-
able, and may even be desirable in some cases.
2.1.3.3 Invertible Systems
When it is possible to build a mapping that recovers the input signals of a
given system from its output, we say that such a system is invertible. This
means that it is possible to obtain
x
from
y
using an inverse system cas-
caded with the original one. This notion will be revisited when we analyze
the problems of equalization and source separation.
2.1.3.4 Stable Systems
Stability is also a major concern in system analysis. We shall assume that
a system is stable if the response to a bounded input is also bounded. In
simple words, if the input signal does not diverge to infinity, the output
will not diverge as well. Stability is a common feature in real-world systems,
which we suppose to be restricted by conservation laws, but the same may
not occur in some mathematical models and algorithms.
